A code-independent performance bound for a given absorbing set is derived for quantized low-density parity-check (LDPC) decoders. The analysis demonstrates that each absorbing set in the Tanner graph imposes a specific lower bound on the frame error rate (FER) of any code containing that absorbing set under a given quantization scheme. This approach is applicable to any message-passing (MP) decoding algorithm and any uniform or non-uniform quantization scheme for LDPC codes. Simulation results using the sum-product algorithm (SPA) provide FERs that are consistent with the obtained bounds. In addition, the bounds demonstrate that the conventional quantized SPA is not capable of achieving very low FERs if the LDPC codes contain certain absorbing sets.
A code-independent performance bound for a given absorbing set is derived for quantized low-density parity-check (LDPC) decoders. The analysis demonstrates that each absorbing set in the Tanner graph imposes a specific lower bound on the frame error rate (FER) of any code containing that absorbing set under a given quantization scheme. This approach is applicable to any message-passing (MP) decoding algorithm and any uniform or non-uniform quantization scheme for LDPC codes. Simulation results using the sum-product algorithm (SPA) provide FERs that are consistent with the obtained bounds. In addition, the bounds demonstrate that the conventional quantized SPA is not capable of achieving very low FERs if the LDPC codes contain certain absorbing sets.
The performance of low-density parity-check (LDPC) codes at high signal-to-noise ratios (SNRs) is known to be limited by the presence of certain sub-graphs that exist in the Tanner graph representation of the code, for example trapping sets and absorbing sets. This paper derives a lower bound on the frame error rate (FER) of any LDPC code containing a given problematic sub-graph, assuming a particular message passing decoder and decoder quantization. A crucial aspect of the lower bound is that it is code-independent, in the sense that it can be derived based only on a problematic sub-graph and then applied to any code containing it. Due to the complexity of evaluating the exact bound, assumptions are proposed to approximate it, from which we can estimate decoder performance. Simulated results obtained for both the quantized sum-product algorithm (SPA) and the quantized min-sum algorithm (MSA) are shown to be consistent with the approximate bound and the corresponding performance estimates. Different classes of LDPC codes, including both structured and randomly constructed codes, are used to demonstrate the robustness of the approach.
The performance of low-density parity-check (LDPC) codes at high signal-to- noise ratios (SNRs) is known to be limited by the presence of certain sub-graphs that exist in the Tanner graph representation of the code, for example trapping sets and absorbing sets. This dissertation derives a lower bound on the frame error rate (FER) of any LDPC code containing a given problematic sub-graph, assuming a particular iterative message passing (MP) decoder and decoder quantization. A crucial aspect of the lower bound is that it is code-independent, in the sense that it can be derived based only on a problematic sub-graph and then applied to any code containing it. Due to the complexity of evaluating the exact bound, assumptions are proposed to approximate it, from which we can estimate decoder performance. For LDPC codes, the attenuated min-sum algorithm (AMSA) and the offset min- sum algorithm (OMSA) are known to outperform the conventional min-sum algorithm (MSA) at low SNRs, i.e., in the waterfall region of the FER curve. This dis- sertation demonstrates that, for quantized LDPC decoders, the AMSA and OMSA underperform the MSA at high SNRs, i.e., in the error floor region of the FER curve, and that the MSA, AMSA, and OMSA all suffer from a relatively high error floor. Therefore, we introduce a novel modification of the MSA for quantized decoding of LDPC codes, called the threshold attenuated min-sum algorithm (TAMSA) (or the threshold offset min-sum algorithm (TOMSA)) with the aim of outperforming the MSA, AMSA, and OMSA at both low and high SNRs. The new decoding algorithm is designed based on the common assumption that trapping sets are the major cause of the error floor for quantized LDPC decoders, and it is shown to reduce the error probability associated with these problematic graphic objects. The lower bound analysis tool noted above is then used to verify the effectiveness of the new TAMSA (TOMSA) and also to assist in finding its optimum design parameters. We also show that the implementation complexity of the TAMSA (TOMSA) is only slightly higher than that of the AMSA or OMSA. Finally, we extend the lower bound to sliding window (SW) decoding of spatially coupled LDPC (SC-LDPC) codes. Additionally, we show that the performance of the TAMSA (TOMSA) is better than that of the MSA, AMSA, and OMSA for SW.
Previously published lower bounds on the error-floor performance of low-density parity-check (LDPC) codes with quantized sum-product algorithm (SPA) decoders need modification to apply to min-sum algorithm (MSA) decoders. In this paper we show that, due to the sub-optimality of MSA decoders, certain assumptions that apply to SPA decoders are not valid for MSA decoders. Based on appropriately modified assumptions, an improved technique is then proposed to evaluate lower bounds on the error floor performance of LDPC codes for an additive white Gaussian noise channel and a quantized MSA decoder. This new technique not only results in error floor bounds for MSA decoders, but also for SPA decoders. The obtained bound is based on an absorbing set, and a good error floor approximation can be obtained when the multiplicity of the absorbing set is known.
Very high data rates and decoding computational complexity place strict constraints in 5G and 6G communications. In this paper, non-uniform Quantized Decoding algorithm is proposed for Low-density Parity Check codes (LDPC). In the proposed algorithm, the check node updating process is carried out using quantization, which reduces complexity. The Sum Product Algorithm (SPA) is iterative message passing decoding techniques offer the optimal performance for LDPC codes. Implementations use message-passing decoding with more precision, results extremely high complexity. In Iterative, message-passing (MP), trapping sets and absorbing sets causes low error floor. In this article non-uniform quantization proposed to overcome dynamic range of values over uniform quantization. Simulation results provide coding gain increases closer to of 0.5 dB in higher SNR and has good error floor at 10−5.
Absorbing sets are known to be the primary factor in the error-floor performance of low-density parity-check (LDPC) codes with message passing decoders over the additive white Gaussian noise (AWGN) channel. Besides showing excellent waterfall performance, spatially coupled LDPC (SC-LDPC) codes that are constructed by an edge spreading technique are known to have fewer cycles and absorbing sets than their block code counterparts, and therefore to exhibit better error-floor performance. Based on our previously obtained results for quantized LDPC block decoders, we derive lower bounds on the performance of quantized SC-LDPC decoders, including both a flooding schedule decoder and a sliding window decoder. Numerical simulation results confirm the accuracy of the obtained bounds and show that, for quantized decoders, properly designed SC-LDPC codes have better error-floor performance than their underlying LDPC block codes.
The error floor phenomenon observed with LDPC codes and their graph-based, iterative, message-passing (MP) decoders is commonly attributed to the existence of error-prone substructures - variously referred to as near-codewords, trapping sets, absorbing sets, or pseudocodewords - in a Tanner graph representation of the code. Many approaches have been proposed to lower the error floor by designing new LDPC codes with fewer such substructures or by modifying the decoding algorithm. Using a theoretical analysis of iterative MP decoding in an idealized trapping set scenario, we show that a contributor to the error floors observed in the literature may be the imprecise implementation of decoding algorithms and, in particular, the message quantization rules used. We then propose a new quantization method - (q+1)-bit quasi-uniform quantization - that efficiently increases the dynamic range of messages, thereby overcoming a limitation of conventional quantization schemes. Finally, we use the quasi-uniform quantizer to decode several LDPC codes that suffer from high error floors with traditional fixed-point decoder implementations. The performance simulation results provide evidence that the proposed quantization scheme can, for a wide variety of codes, significantly lower error floors with minimal increase in decoder complexity.